摘要
We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. One pair has each component of its velocity field to be approximated by the P-1 nonconforming quadrilateral element while the pressure field is approximated by the piecewise constant function with globally two-dimensional subspaces removed: one removed space is due to the integral mean-zero property and the other space consists of global checker-board patterns. The other pair consists of the velocity space as the P-1 nonconforming quadrilateral element enriched by a globally one-dimensional macro bubble function space based on DSSY (Douglas-Santos-Sheen-Ye) nonconforming finite element space; the pressure field is approximated by the piecewise constant function with mean-zero space eliminated. We show that two element pairs satisfy the discrete inf-sup condition uniformly. And we investigate the relationship between them. Several numerical examples are shown to confirm the efficiency and reliability of the proposed methods.
- 出版日期2016-6